Product portfolio optimization (PPO) is a strategic decision for many organizations. There are several technical methods for facilitating this decision. According to the reviewed studies, the implementation of the robust optimization approach and the invasive weed optimization (IWO) algorithm is the research gap in this field. The contribution of this paper is the development of the PPO problem with the help of the robust optimization approach and the multi-objective IWO algorithm. Considering the profit margin uncertainty in real-world investment decisions, the robust optimization approach is used to address this issue. To illustrate the real-world applicability of the model, it is implemented for dairy products of Pegah Golpayegan Company in Iran. The numerical results obtained from the IWO algorithm demonstrate the effectiveness of the proposed algorithm in tracing out the efficiency frontier of the product portfolio. The average risk of efficient frontier solutions in the deterministic model is about 0.4 and for the robust counterpart formulation is at least 0.5 per product. The efficient frontier solutions obtained from robust counterpart formulation demonstrate a more realistic risk level than the deterministic model. The comparisons between CPLEX, IWO and genetic algorithm (GA) shows that the performance of the IWO algorithm is much better than the older algorithms and can be considered as an alternative to algorithms, such as GA in product portfolio optimization problems.